800 900 1000 1100 1200 1300 1400 1500 X (m)
0 100 200 300 400
Y(m)
0 1 2 3 4
Curvinessc (rad)
14
13 12
11
9 10 8
7
5 6
4
3
2 1
Figure 3.9 – Results of the road curve estimator.
profiles.
Table 3.4– Properties of the classified road curves.
Road curve No.
Property 1 2 3 4 5 6 7 8 9 10 11 12 13 14
¯
rc(m) 43 49 35 98 38 77 35 42 70 35 61 33 28 30
¯
γ(◦) 113 85 254 119 218 103 208 78 74 112 182 184 237 130 c(rad)×10−2 169 123 388 226 358 181 319 117 114 166 408 319 396 207
1060 1080 1100 1120 1140 1160
X (m)
140 160 180 200 220 240
Y (m )
¯
r
c= 35m
¯
γ = 208
◦c = 3 . 19rad GPS
Curve Detection Classi fi cation Result
Figure 3.10– Properties of road curve No. 7.
identified by the curve estimator, which indicates the robustness of the developed algorithm. The particular curve properties mean curve radiusr¯c, mean curve angle
¯
γ, and curvinesscare illustrated in Table 3.4. It can also be seen that the distorted curve No. 11 was scored with a high curviness even if the mean curve angle ¯γ was scored not that high in comparison to the other curves. This manifests the proposed index curvinesscas an curve-evaluation index.
Figure3.10shows the classification results of curve No. 7 in more detail. The curve estimator detected the correct beginning and end of the curvature of the road, which is represented by the solid line (Curve Detection). In addition, the estimated curve properties are highlighted with a circular arc with geometric dimensions according to the estimation results (Classification Result). It can be seen that the estimated circular arc roughly fits to the real road curvature. The overestimation is a result
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
X (km)
0 0.2 0.4
Y(km)
0 2 4 6 8 9 11 13 15 17
Road Curviness C (rad)
5 4
3 2
1
Figure 3.11– Results of the road curviness classification.
of the curve construction with clothoids, as can be seen at the beginning and end of the curve in Figure 3.10. These parts also contribute to the estimation algorithm.
The calculation of the running mean of the roll angle results in curve properties that are a compromise between the smallest curve radius and the clothoids of the curve. The proposed method is well suited to detect and classify curves in order to collect customer usage profiles and to evaluate the driven curves. In addition, the road curvinessCcontinuously scores road segments ofl= 1 km, as illustrated in Figure3.11. It can be seen that the road curviness scores the respective road segment depending on the amount and curviness of curves within the segment. The road curvinessCwas scored to 9,11,15,17, and6(rounded) for the given road segments No. 1–5. Road segment No. 4 was scored with the highest road curviness C. This is reasonable due to the amount of sharp curves within the segment. In contrast to the single curve classification, the continuous classification of road segments makes a characterisation of the driven roads possible.
The lumped-mass model achieved sufficient results for the scope of customer usage profiles. The classified curve properties can be counted online, whereas the number of gradations is chosen by the user and the memory capacities. Since the algorithm is based on the response of the vehicle, the estimated curve properties are based on the driving line of the motorcycle. Thus, different curve driving techniques can lead to different results for the same curve. The differences are assumed to be negligible
600 700 800 900
Altitude(m)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Distance (km)
-50 0 50
H(m/km) Hp
Hn
Figure 3.12– Results of the road slope classification.
in terms of customer usage profiles.
3.6.2 Road slope classification
The road slope estimator developed by Gorges et al. was validated with the help of a mountain road in a previous publication [1]. In the present paper, this mountain road has been utilised to show the results of the road slope classification method.
The mountain road was driven uphill and downhill with the reference motorcycle, as shown in the upper plot of Figure3.12. The counting results of the road hilliness H are illustrated in the bottom plot for positive and negative values, respectively.
The road hilliness H counts the positive and negative elevation gain per kilometre.
The overall elevation gain for this ride was counted tohp= 342 mandhn=−343 m.
Once the road slope estimator is implemented in the vehicle, it is convenient to count the elevation gain with the presented method. The distribution of an overall elevation gain as part of the customer usage profiles is favourable for the vehicle development process, since it affects vehicle design targets and improves the understanding of
the customer behaviour. The travelled elevation gain has a direct influence on the powertrain design and on the brake design. In addition, the classification of the particular road segments improves the choice of real test road or for the design of virtual test tracks.
3.6.3 Validation of the road profile estimator
Real roads are not characterised by a homogeneous road class, as highlighted by Andrén [39] and Bogsjö [42, 43]. Furthermore, arbitrary roads are in general not surveyed by a road profiler, which makes a validation infeasible. For this reasons, the validation of the road profile estimator was achieved by numerical simulation, for which the full-vehicle model was excited by the pseudo-random test track as presented in Section 3.5.2. The simulation was performed by the ode45-solver of MATLAB⃝R, which is based on the Runge–Kutta method. Each of the eight road class segments (A–H) was travelled with a constant acceleration of the motorcycle.
This guarantees that the estimator was tested under variable velocities and that all possible frequencies in the range of use have been excited. The maximum velo-cities vmax for the respective road classes were chosen with respect to the physical limitations of a motorcycle travelling over the tracks. The minimum velocity is vmin = 3 m s−1, which is the minimum required velocity for the road profile estim-ator. Each road class was driven for a time period oft= 100 s. Since the full-vehicle model has no degree of freedom in the longitudinal direction, the variable velocity was realised through the transformation of the road profile from the spatial domain to the time domain. Figure3.13shows the results of the simulation. The upper plot shows the linear slope of the velocity v in every road class segment together with the maximum velocities vmax, respectively. The last three road classes (F–G) were driven with a maximum velocity of vmax = 5 m s−1 because they represent heavy off-road tracks which are difficult to ride even for an enduro motorcycle like the reference vehicle. The middle plot shows the respective road profile zR(t). It gets rougher with an increase in the road class. The bottom plot shows the classification results of the road profile estimator. It can be seen that almost all predicted road classes are classified correctly. The time span was set to ∆tbuf = 1 s. This means that 100 time segments have been classified per road class. A total of four estimates have been classified false, but only by a one road-class difference. This indicates that
0 10 20 30 50 60
Velocityv(m/s) Actual Class
A B C D E F G H
-1 0 1
zR(m)
0 100 200 300 400 500 600 700 800
Timet (s)
A B C D E F G H
PredictedClass
Figure 3.13– Validation of the road profile estimator.
the proposed method is robust and highly accurate. As is common in classification analysis, the results are reported in a confusion matrix, see Table3.5.
The entries contain the amount of respective classifications. The last row and column illustrate the percentage of correct classified values in each class. An overall classification result of99.5 %was achieved. A higher time span∆tbufleads to a more robust result, since the signal length and thus the frequency content gets higher. On the other hand, under the assumption of a variable velocity, the transfer function gets ambiguous and therefore the classification quality gets worse. Additionally, the road quality can change very fast, so that a longer time period results in an indistinct classification result. In the end, the choice of the time span∆tbuf is a compromise between reaction speed and quality. The underlying method of the PSD calculation has also an influence on the classification result. Since the smoothing algorithm
Table 3.5– Confusion matrix of the road profile estimator.
Actual class
A B C D E F G H ∑
(%)
Predictedclass
A 100 0 0 0 0 0 0 0 100
B 0 100 0 0 0 0 0 0 100
C 0 0 100 0 0 0 0 0 100
D 0 0 0 100 0 0 0 0 100
E 0 0 0 0 100 1 0 0 99
F 0 0 0 0 0 98 1 0 99
G 0 0 0 0 0 1 99 1 98
H 0 0 0 0 0 0 0 99 100
∑(%) 100 100 100 100 100 98 99 99 99.5
is applied after the PSD calculation, an overlapped PSD calculation method is not necessary to achieve a robust result. In addition, this would lead to a loss of frequency resolution, which is essential for the road classification algorithm.
The results show that the frequency approach is successful and highly accurate even under variable velocity, which had been addressed as a disadvantage of this method in the past [20, 21, 23]. The reaction time is fast enough for collecting customer usage profiles and implementing it into real-time control systems. Furthermore, the modular approach makes the presented method easily extensible depending on the available onboard sensors. In addition, the computational effort is less compared to the alternative methods. An online application is therefore feasible. The developed road profile estimator requires a full-vehicle model of the motorcycle, the velocity v, and at least one suspension deflection signal as input. The derivation of transfer functions requires an LTI system formulation. Thus, the model has to be reduced to a linear system.